X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Funfold%2Fltpss_tpss.ma;h=24f1a595e65961a608d6299aa2e1de97cc44c6d1;hb=011cf6478141e69822a5b40933f2444d0522532f;hp=b8e425e631ab4908119467123776d588344edae6;hpb=55dc00c1c44cc21c7ae179cb9df03e7446002c46;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma
index b8e425e63..24f1a595e 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma
@@ -12,158 +12,158 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic-2/unfold/tpss_ltps.ma".
-include "Basic-2/unfold/ltpss.ma".
+include "Basic_2/unfold/tpss_ltps.ma".
+include "Basic_2/unfold/ltpss.ma".
 
 (* PARTIAL UNFOLD ON LOCAL ENVIRONMENTS *************************************)
 
 (* Properties concerning partial unfold on terms ****************************)
 
-lemma ltpss_tpss_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ≫* L0 →
-                           ∀T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫* U2 →
-                           d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ≫* U2.
+lemma ltpss_tpss_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
+                           ∀T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶* U2 →
+                           d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ▶* U2.
 #L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0 //
 #L #L0 #_ #HL0 #IHL #T2 #U2 #d2 #e2 #HTU2 #Hde1d2
-lapply (ltps_tpss_trans_ge … HL0 HTU2) -HL0 HTU2 /2/
+lapply (ltps_tpss_trans_ge … HL0 HTU2) -HL0 -HTU2 /2 width=1/
 qed.
 
-lemma ltpss_tps_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ≫* L0 →
-                          ∀T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫ U2 →
-                          d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ≫* U2.
+lemma ltpss_tps_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
+                          ∀T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
+                          d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ▶* U2.
 #L1 #L0 #d1 #e1 #HL10 #T2 #U2 #d2 #e2 #HTU2 #Hde1d2
-@(ltpss_tpss_trans_ge … HL10 … Hde1d2) /2/ (**) (* /3 width=6/ is too slow *)
+@(ltpss_tpss_trans_ge … HL10 … Hde1d2) /2 width=1/ (**) (* /3 width=6/ is too slow *)
 qed.
 
-lemma ltpss_tpss_trans_eq: ∀L0,L1,d,e. L0 [d, e] ≫* L1 →
-                           ∀T2,U2. L1 ⊢ T2 [d, e] ≫* U2 → L0 ⊢ T2 [d, e] ≫* U2.
+lemma ltpss_tpss_trans_eq: ∀L0,L1,d,e. L0 [d, e] ▶* L1 →
+                           ∀T2,U2. L1 ⊢ T2 [d, e] ▶* U2 → L0 ⊢ T2 [d, e] ▶* U2.
 #L0 #L1 #d #e #H @(ltpss_ind … H) -L1
-[ /2/
+[ /2 width=1/
 | #L #L1 #_ #HL1 #IHL #T2 #U2 #HTU2
-  lapply (ltps_tpss_trans_eq … HL1 HTU2) -HL1 HTU2 /2/
+  lapply (ltps_tpss_trans_eq … HL1 HTU2) -HL1 -HTU2 /2 width=1/
 ]
 qed.
 
-lemma ltpss_tps_trans_eq: ∀L0,L1,d,e. L0 [d, e] ≫* L1 →
-                          ∀T2,U2. L1 ⊢ T2 [d, e] ≫ U2 → L0 ⊢ T2 [d, e] ≫* U2.
-/3/ qed.
+lemma ltpss_tps_trans_eq: ∀L0,L1,d,e. L0 [d, e] ▶* L1 →
+                          ∀T2,U2. L1 ⊢ T2 [d, e] ▶ U2 → L0 ⊢ T2 [d, e] ▶* U2.
+/3 width=3/ qed.
 
 lemma ltpss_tpss_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 → 
-                          L0 ⊢ T2 [d2, e2] ≫* U2 → L0 [d1, e1] ≫* L1 →
-                          L1 ⊢ T2 [d2, e2] ≫* U2.
+                          L0 ⊢ T2 [d2, e2] ▶* U2 → L0 [d1, e1] ▶* L1 →
+                          L1 ⊢ T2 [d2, e2] ▶* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HTU2 #H @(ltpss_ind … H) -L1
 [ //
 | -HTU2 #L #L1 #_ #HL1 #IHL
-  lapply (ltps_tpss_conf_ge … HL1 IHL) -HL1 IHL //
+  lapply (ltps_tpss_conf_ge … HL1 IHL) -HL1 -IHL //
 ]
 qed.
 
 lemma ltpss_tps_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 → 
-                         L0 ⊢ T2 [d2, e2] ≫ U2 → L0 [d1, e1] ≫* L1 →
-                         L1 ⊢ T2 [d2, e2] ≫* U2.
+                         L0 ⊢ T2 [d2, e2] ▶ U2 → L0 [d1, e1] ▶* L1 →
+                         L1 ⊢ T2 [d2, e2] ▶* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HTU2 #HL01
-@(ltpss_tpss_conf_ge … Hde1d2 … HL01) /2/ (**) (* /3 width=6/ is too slow *)
+@(ltpss_tpss_conf_ge … Hde1d2 … HL01) /2 width=1/ (**) (* /3 width=6/ is too slow *)
 qed.
 
 lemma ltpss_tpss_conf_eq: ∀L0,L1,T2,U2,d,e.
-                          L0 ⊢ T2 [d, e] ≫* U2 → L0 [d, e] ≫* L1 →
-                          ∃∃T. L1 ⊢ T2 [d, e] ≫* T & L1 ⊢ U2 [d, e] ≫* T.
+                          L0 ⊢ T2 [d, e] ▶* U2 → L0 [d, e] ▶* L1 →
+                          ∃∃T. L1 ⊢ T2 [d, e] ▶* T & L1 ⊢ U2 [d, e] ▶* T.
 #L0 #L1 #T2 #U2 #d #e #HTU2 #H @(ltpss_ind … H) -L1
-[ /2/
+[ /2 width=3/
 | -HTU2 #L #L1 #_ #HL1 * #W2 #HTW2 #HUW2
   elim (ltps_tpss_conf … HL1 HTW2) -HTW2 #T #HT2 #HW2T
-  elim (ltps_tpss_conf … HL1 HUW2) -HL1 HUW2 #U #HU2 #HW2U
-  elim (tpss_conf_eq … HW2T … HW2U) -HW2T HW2U #V #HTV #HUV
-  lapply (tpss_trans_eq … HT2 … HTV) -T;
-  lapply (tpss_trans_eq … HU2 … HUV) -U /2/
+  elim (ltps_tpss_conf … HL1 HUW2) -HL1 -HUW2 #U #HU2 #HW2U
+  elim (tpss_conf_eq … HW2T … HW2U) -HW2T -HW2U #V #HTV #HUV
+  lapply (tpss_trans_eq … HT2 … HTV) -T
+  lapply (tpss_trans_eq … HU2 … HUV) -U /2 width=3/
 ]
 qed.
 
 lemma ltpss_tps_conf_eq: ∀L0,L1,T2,U2,d,e.
-                         L0 ⊢ T2 [d, e] ≫ U2 → L0 [d, e] ≫* L1 →
-                         ∃∃T. L1 ⊢ T2 [d, e] ≫* T & L1 ⊢ U2 [d, e] ≫* T.
-/3/ qed.
+                         L0 ⊢ T2 [d, e] ▶ U2 → L0 [d, e] ▶* L1 →
+                         ∃∃T. L1 ⊢ T2 [d, e] ▶* T & L1 ⊢ U2 [d, e] ▶* T.
+/3 width=3/ qed.
 
-lemma ltpss_tpss_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≫* T2 →
-                       ∀L2,ds,es. L1 [ds, es] ≫* L2 → 
-                       ∃∃T. L2 ⊢ T1 [d, e] ≫* T & L1 ⊢ T2 [ds, es] ≫* T.
+lemma ltpss_tpss_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ▶* T2 →
+                       ∀L2,ds,es. L1 [ds, es] ▶* L2 → 
+                       ∃∃T. L2 ⊢ T1 [d, e] ▶* T & L1 ⊢ T2 [ds, es] ▶* T.
 #L1 #T1 #T2 #d #e #HT12 #L2 #ds #es #H @(ltpss_ind … H) -L2
-[ /3/
+[ /3 width=3/
 | #L #L2 #HL1 #HL2 * #T #HT1 #HT2
   elim (ltps_tpss_conf … HL2 HT1) -HT1 #T0 #HT10 #HT0
-  lapply (ltps_tpss_trans_eq … HL2 … HT0) -HL2 HT0 #HT0
-  lapply (ltpss_tpss_trans_eq … HL1 … HT0) -HL1 HT0 #HT0
-  lapply (tpss_trans_eq … HT2 … HT0) -T /2/
+  lapply (ltps_tpss_trans_eq … HL2 … HT0) -HL2 -HT0 #HT0
+  lapply (ltpss_tpss_trans_eq … HL1 … HT0) -HL1 -HT0 #HT0
+  lapply (tpss_trans_eq … HT2 … HT0) -T /2 width=3/
 ]
 qed.
 
-lemma ltpss_tps_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≫ T2 →
-                      ∀L2,ds,es. L1 [ds, es] ≫* L2 → 
-                      ∃∃T. L2 ⊢ T1 [d, e] ≫* T & L1 ⊢ T2 [ds, es] ≫* T.
-/3/ qed.
+lemma ltpss_tps_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ▶ T2 →
+                      ∀L2,ds,es. L1 [ds, es] ▶* L2 → 
+                      ∃∃T. L2 ⊢ T1 [d, e] ▶* T & L1 ⊢ T2 [ds, es] ▶* T.
+/3 width=1/ qed.
 
 (* Advanced properties ******************************************************)
 
 lemma ltpss_tps2: ∀L1,L2,I,e.
-                  L1 [0, e] ≫* L2 → ∀V1,V2. L2 ⊢ V1 [0, e] ≫ V2 →
-                  L1. 𝕓{I} V1 [0, e + 1] ≫* L2. 𝕓{I} V2.
+                  L1 [0, e] ▶* L2 → ∀V1,V2. L2 ⊢ V1 [0, e] ▶ V2 →
+                  L1. ⓑ{I} V1 [0, e + 1] ▶* L2. ⓑ{I} V2.
 #L1 #L2 #I #e #H @(ltpss_ind … H) -L2
-[ /3/
+[ /3 width=1/
 | #L #L2 #_ #HL2 #IHL #V1 #V2 #HV12
   elim (ltps_tps_trans … HV12 … HL2) -HV12 #V #HV1 #HV2
-  lapply (IHL … HV1) -IHL HV1 #HL1
+  lapply (IHL … HV1) -IHL -HV1 #HL1
   @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
 ]
 qed.
 
 lemma ltpss_tps2_lt: ∀L1,L2,I,V1,V2,e.
-                     L1 [0, e - 1] ≫* L2 → L2 ⊢ V1 [0, e - 1] ≫ V2 →
-                     0 < e → L1. 𝕓{I} V1 [0, e] ≫* L2. 𝕓{I} V2.
+                     L1 [0, e - 1] ▶* L2 → L2 ⊢ V1 [0, e - 1] ▶ V2 →
+                     0 < e → L1. ⓑ{I} V1 [0, e] ▶* L2. ⓑ{I} V2.
 #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He
->(plus_minus_m_m e 1) /2/
+>(plus_minus_m_m e 1) // /2 width=1/
 qed.
 
-lemma ltpss_tps1: ∀L1,L2,I,d,e. L1 [d, e] ≫* L2 →
-                  ∀V1,V2. L2 ⊢ V1 [d, e] ≫ V2 →
-                  L1. 𝕓{I} V1 [d + 1, e] ≫* L2. 𝕓{I} V2.
+lemma ltpss_tps1: ∀L1,L2,I,d,e. L1 [d, e] ▶* L2 →
+                  ∀V1,V2. L2 ⊢ V1 [d, e] ▶ V2 →
+                  L1. ⓑ{I} V1 [d + 1, e] ▶* L2. ⓑ{I} V2.
 #L1 #L2 #I #d #e #H @(ltpss_ind … H) -L2
-[ /3/
+[ /3 width=1/
 | #L #L2 #_ #HL2 #IHL #V1 #V2 #HV12
   elim (ltps_tps_trans … HV12 … HL2) -HV12 #V #HV1 #HV2
-  lapply (IHL … HV1) -IHL HV1 #HL1
+  lapply (IHL … HV1) -IHL -HV1 #HL1
   @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
 ]
 qed.
 
 lemma ltpss_tps1_lt: ∀L1,L2,I,V1,V2,d,e.
-                     L1 [d - 1, e] ≫* L2 → L2 ⊢ V1 [d - 1, e] ≫ V2 →
-                     0 < d → L1. 𝕓{I} V1 [d, e] ≫* L2. 𝕓{I} V2.
+                     L1 [d - 1, e] ▶* L2 → L2 ⊢ V1 [d - 1, e] ▶ V2 →
+                     0 < d → L1. ⓑ{I} V1 [d, e] ▶* L2. ⓑ{I} V2.
 #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #Hd
->(plus_minus_m_m d 1) /2/
+>(plus_minus_m_m d 1) // /2 width=1/
 qed.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma ltpss_fwd_tpsa21: ∀e,K1,I,V1,L2. 0 < e → K1. 𝕓{I} V1 [0, e] ≫* L2 →
-                        ∃∃K2,V2. K1 [0, e - 1] ≫* K2 & K1 ⊢ V1 [0, e - 1] ≫* V2 &
-                                 L2 = K2. 𝕓{I} V2.
+lemma ltpss_fwd_tpss21: ∀e,K1,I,V1,L2. 0 < e → K1. ⓑ{I} V1 [0, e] ▶* L2 →
+                        ∃∃K2,V2. K1 [0, e - 1] ▶* K2 & K1 ⊢ V1 [0, e - 1] ▶* V2 &
+                                 L2 = K2. ⓑ{I} V2.
 #e #K1 #I #V1 #L2 #He #H @(ltpss_ind … H) -L2
 [ /2 width=5/
-| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct -L;
+| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct
   elim (ltps_inv_tps21 … HL2 ?) -HL2 // #K2 #V2 #HK2 #HV2 #H
   lapply (ltps_tps_trans_eq … HV2 … HK2) -HV2 #HV2
   lapply (ltpss_tpss_trans_eq … HK1 … HV2) -HV2 #HV2 /3 width=5/
 ]
-qed.
+qed-.
 
-lemma ltpss_fwd_tpss11: ∀d,e,I,K1,V1,L2. 0 < d → K1. 𝕓{I} V1 [d, e] ≫* L2 →
-                        ∃∃K2,V2. K1 [d - 1, e] ≫* K2 &
-                                 K1 ⊢ V1 [d - 1, e] ≫* V2 &
-                                 L2 = K2. 𝕓{I} V2.
+lemma ltpss_fwd_tpss11: ∀d,e,I,K1,V1,L2. 0 < d → K1. ⓑ{I} V1 [d, e] ▶* L2 →
+                        ∃∃K2,V2. K1 [d - 1, e] ▶* K2 &
+                                 K1 ⊢ V1 [d - 1, e] ▶* V2 &
+                                 L2 = K2. ⓑ{I} V2.
 #d #e #K1 #I #V1 #L2 #Hd #H @(ltpss_ind … H) -L2
 [ /2 width=5/
-| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct -L;
+| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct
   elim (ltps_inv_tps11 … HL2 ?) -HL2 // #K2 #V2 #HK2 #HV2 #H
   lapply (ltps_tps_trans_eq … HV2 … HK2) -HV2 #HV2
   lapply (ltpss_tpss_trans_eq … HK1 … HV2) -HV2 #HV2 /3 width=5/
 ]
-qed.
+qed-.